Measure of Entropy Change

Entropy means the transformation of the state of the system by the change of thermal energy or heat per unit temperature which measure the amount of unavailable energy for doing useful work, entropy also measure the molecular disorder or chaotic randomness motion of a system. The concept of entropy obtained from the second law of thermodynamics in chemistry and unreliable energy in the Carnot cycle by the specific heat transfer.

Higher the randomness greater will be the entropy. A system passes spontaneously from more orderliness to less orderliness. If the system is left to change its state spontaneously, it passes to the more chaotic state and the process of change state stops when the system attains a maximum chaotic state.

Entropy change, heat change and unavailable energy in Carnot cycle

Therefore for a spontaneous process, the entropy will be increasing and process to attain equilibrium when the entropy will attain maximum value. Net entropy means the sum of the entropy of the system and surroundings. Thus we can two laws of thermodynamics

  1. From the first law of thermodynamics, the net energy of the universe is constant.
  2. From the second law thermodynamics, the net entropy change of the universe is increasing.

Definition of Entropy Change

Clausius definition of entropy (s) is a state function and its change of a system, he defined as

ds = dqr/T

Therefore according to Clausius equation in chemistry, heat transfer that occurs reversibly/temperature change occurs is called the entropy of the system.

When heat change occurs in different temperatures,

    \[ \boxed{ds = \frac{dq_{1}}{T_{1}} + \frac{dq_{2}}{T_{2}} + ... =\int_{T_{1}}^{T_{2}}\frac{dq_{r}}{T}} \]

Work Done in Carnot Cycle

The can’t cycle operates in reversible paths. Let us take dq1 heat from HTR at T1 and rejected dq2 heat to LTR at T2.

Now let us consider the quantity, heat change/temperature from the above diagram

  • A ⇒ C via B, heat change/ temp = dq1/T1 + 0 = dq1/T1
  • A ⇒ C via D, heat change/ temp = 0 + dq1/T1 = dq2/T2

But can’t cycles states
dq1/T1 = dq2/T2

Hence we can conclude that heat change/temperature is the same for the change of two definite states and independent of path change.

From the whole cycles of operation, heat change/temperature,

= dq1/T1 + 0 – dq2/T2 + 0 = 0

Therefore, heat change /temperature is a fundamental property and a state function.

Unavailable Energy in Thermodynamics

From the can’t cycles,
dq1/T1 = dq2/T2
where dq1 energy supplied to the can’t cycle at temp T1.

But can’t cycle fails to convert dq2 heat into useful work and rejected to the sink at T2. Therefore, the unavailable energy for the cycle = dq2.

Thus the unavailable energy equation of the cycle = temp of the system after conversion into heat × entropy increases due to energy take up.

Therefore, when a system absorbed a certain amount of heat in the reversible process a part of absorbed energy can utilize for producing work. While the remaining part goes to increases the randomness of the molecules and thereby increases the entropy of the system.